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Free Space Optics (FSO) links are affected by several impairments: optical turbulence, scattering, absorption, and pointing. In particular, atmospheric optical turbulence generates optical power fluctuations at the receiver that can degrade communications with fading events, especially in high data rate links. Innovative solutions require an improvement of FSO link performances, together with testing models and appropriate channel codes. In this paper, we describe a high-resolution time-correlated channel model able to predict random temporal fluctuations of optical signal irradiance caused by optical turbulence. Concerning the same channel, we also report simulation results on the error mitigation performance of Luby Transform, Raptor, and RaptorQ codes.

FSO is an optical wireless line-of-sight communication system able to offer good broadband performances, electromagnetic interference immunity, high security, license-free operation, low power consumption, ease of relocation, and straightforward installation [

Thanks to these features, FSO is suitable for different broadband telecom applications as airborne, satellite scenarios, Next Generation Networks (NGN), and, finally, “Last Mile” communication links. In addition, FSO bandwidth performance can be further improved by using Wavelength Division Multiplexing (WDM) techniques reaching over 1.28 Tbps capacity [

Unfortunately, as the transmission medium in a terrestrial FSO link is the air, these communications are strongly dependent on various atmospheric phenomena (as rain, snow, optical turbulence, and especially fog) that can cause losses and fading. Therefore, in worst-case conditions, it could be necessary to increase the optical transmission power although, at the same time, it is needed to comply with safety regulations. The commonly used wavelengths in outdoor FSO communications are 830, 1064, and 1550 nm, but, for the previously mentioned reasons, the highest is preferred for transmission [

Current laser technologies offer high-power sources at the most important wavelengths for communications. Novel technologies enable us to improve several applications previously limited by the fixed wavelength and power of other laser technologies. Today, we no longer have to work around the closest fit wavelength, but we can find the best wavelength to fit FSO communications [

The effects of already mentioned impairments are scattering (i.e., Rayleigh and Mie) losses, absorption, and scintillation. The first two can be described by proper attenuation coefficients [

Therefore, due to the scintillation, in FSO links the irradiance fluctuates and could drop below a threshold under which the receiver is not able to detect the useful signal. In this case, communications suffer from cancellation errors, which cause link outages. This phenomenon becomes relevant at high distance, but it can also be observed in 500 m long FSO links. Moreover, the optical turbulence intensity can change by more than an order of magnitude during the course of a day: it reaches its maximum around midday (when the temperature is the highest) and, conversely, it is lower during the night [

In order to reduce or eliminate these impairments, different methods (hardware and software) were studied and reported in the literature. Hardware solutions focus on aperture averaging effects [

Rateless codes are an innovative solution suitable for channels affected by erasure or burst errors. They add a redundant coding (also settable on the fly) to the source data, allowing the receiver to successfully recover the whole payload that, otherwise, would be corrupted or partially lost.

In order to test rateless codes recovery capabilities in FSO channels, we have to know detailed information about the occurring signal fading, in particular, its depth, temporal duration, and statistics. For this reason, we have implemented a time-correlated channel model able to generate an irradiance time series at the receiver side, at wide range of turbulence conditions (weak to strong).

Generated time series represents a prediction of temporal irradiance fluctuations caused by scintillation. By using the generated data, we were able to test the recovery capabilities of several types of rateless codes. In a previous work [

In particular, we tested Luby Transform (LT) codes [

Several distribution models were developed in the literature to estimate optical turbulence effects (e.g., lognormal, negative exponential models,

Instead, a more versatile model is the Gamma-Gamma distribution, which is able to estimate optical turbulence from weak to moderate-strong fluctuation. This distribution is provided by two independent Gamma statistics which arise, respectively, from large-scale and small-scale atmospheric effects [

For the above-mentioned properties, the Gamma-Gamma model is proper for our applications and it will be better described in Section

The Gamma-Gamma statistics are able to describe the FSO scintillation phenomena in a broad range of turbulence conditions and, for this reason, it is suitable to design our correlated model. The Gamma-Gamma model provides the probability density function (PDF) of received optical irradiance (

Starting from the PDF, we can generate a random irradiance time serie, but it is mandatory to define a temporal correlation relationship between the samples. Assuming a plane-wave propagation, the spatial relationship linking the optical irradiance values is given by the following covariance function:

where _{1}_{1}(

In order to convert the spatial covariance into a time function, we applied Taylor’s

Setting the ^{−1}, thus obtaining irradiance correlation times close to those experimentally and theoretically reported in the literature [

We can simulate predictions of irradiance fluctuations that make use of discrete irradiance time series—following Gamma-Gamma distribution—in which the samples are temporally spaced by one correlation time. The latter can be defined as the time in which the amplitude of normalized covariance function is equal to 0.5 and it represents a time distance beyond which we can consider the samples uncorrelated. The method that we have just described is known as Block Fading Model (BFM) [

The correlation filter employed is created using the Fourier amplitudes associated with the target power spectral density. The block function is memoryless, and this ensures that the spectral properties of the generated signal are not altered during the execution of the algorithm [

In our case, the algorithm input parameters are the double side Fourier transform of the temporal irradiance covariance—obtained through the FFT of

In Figure

Simulated irradiance fluctuations for

Figure

Irradiance covariance function for

Probability density function for

In the BFM the spacing between the irradiance samples equals the correlation time. We generated an irradiance time series according to the BFM, Figure

: (a) Samples distribution histogram and (b) simulated temporal optical irradiance fluctuations in the case of BFM.

In our correlated channel model, for the same values of Rytov variance and time interval, considering a temporal spacing of 10

(a) Samples distribution histogram and (b) simulated temporal optical irradiance fluctuations in the case of correlated model.

At the receiver, the irradiance fluctuations cause communication failures and outages, when irradiance values drop below a fading depth (threshold under which the receiver is not able to detect data). In other words, when the optical signal drops below the above-mentioned fading depth threshold, we interpret it as an erasure error occurring in the FSO communication link.

It is also worth noting that at relatively strong turbulence conditions, power fluctuations become larger and, hence, the average value of the signal power decreases. For these reasons, in our work, we referred to the normalized average value of the signal power and, in particular, to the normalized average value of the irradiance at the receiver.

Using the channel model described in the previous section, we investigated the outage statistics and the performance of rateless codes at fast data rate. In detail, we tested the LT codes and RCs capabilities in order to mitigate erasure errors, which can be detected during a 500 m single terrestrial free space link. In our simulations, we used a 1550 nm wavelength. In addition, we did not consider the noise due to the photodetector, because it can be neglected if compared to the irradiance fluctuations caused by scintillation phenomena in the turbulence conditions taken into account.

In detail, we considered that the photodetector has a Noise Equivalent Power (NEP), that is, the minimum detectable input power, of 6 dB and 9 dB lower (fading depth) than the mean value of the irradiance at the receiver. Consequently, the latter is not constant but varies with the turbulence conditions.

In Figure

Outage statistics histogram for a −9 dB fading depth at a Rytov variance: (a) 0.6; (b) 1.0.

Fountain codes (FCs) are rateless and also suitable for q-ary erasure channels; FSO channels can be described similarly. FCs do not need feedback [

The computational costs of LT codes depend on

Moreover, RCs are systematic codes (i.e., codes in which the first

RQ codes are an evolution of RCs. They are also systematic codes but they work on a much larger alphabet, in particular on GF(256). It can be demonstrated that with a larger alphabet, the failure probability is reduced at a certain overhead [

We tested the performance of LT codes and RCs by simulating an OOK modulated transmission of 100 Mbps (1518 bytes frame size) over a distance of 500 m, at different fading depths and ^{−2}), RCs are able to recover all the source data starting from ^{−3}.

Comparison between LT codes and RCs for the same source packets number and overhead.

However, the best performance is given for

Comparison between LT codes and RCs at constant overhead for the same source packets number.

RQ codes at four

We can see how RQ codes are able to recover all the source data from

We produced a high-resolution FSO channel model that takes into account the temporal covariance of irradiance and hence is able to simulate the temporal irradiance fluctuations at the receiver, with a high resolution. Moreover, it also permits us to set the temporal spacing among the irradiance samples via a proper sampling frequency for the FFT of the temporal irradiance covariance. Our correlated model shows a much larger temporal resolution if compared to the BFM and, for this reason, it is appropriate for communication testing at high data rates.

We also tested, in our channel model, the performance of LT codes and RCs able to mitigate erasure errors caused by the scintillation phenomena. Our simulations illustrate that LT codes, with

This work is supported by the European Space Agency under Grant no. 5401001020. The authors are very grateful to Dr. E. Armandillo for enlightening discussions.